Courtney and Kurtis are planning to travel 160 km in a car by travelling at x kilometres per hour for the first half of the distance, and then increasing their speed by 10 km/h to finish the distance. Which is the correct simplified expression for the total time of the trip?
a)160x+800 divided by x(x+10)
b)80x+800 divided by x(x+10)
c)80x+800 divided by 2x+10
d)160x+800 divided by 2x+10
80/x + 80/(x+10)
(80(x+10)+80x) / x(x+10)
(160x+800) / x(x+10)
To find the total time of the trip, we need to consider the time taken for the first half of the distance and the time taken for the second half of the distance.
Let's start by finding the time taken to travel the first half of the distance :
Distance = Speed × Time
Time = Distance / Speed
For the first half, the distance covered is 160 km / 2 = 80 km, and the speed is x km/h. Therefore, the time taken for the first half of the distance is 80 / x hours.
Now, let's find the time taken to travel the second half of the distance:
The distance covered for the second half is also 80 km. However, the speed for the second half is x + 10 km/h. Therefore, the time taken for the second half of the distance is 80 / (x + 10) hours.
To find the total time, we add the time for the first half and the time for the second half:
Total Time = Time taken for first half + Time taken for second half
= 80 / x + 80 / (x + 10)
To simplify the expression, we find the common denominator and combine the terms:
Total Time = (80(x + 10) + 80x) / (x(x + 10))
= (80x + 800 + 80x) / (x(x + 10))
= (160x + 800) / (x(x + 10))
The correct simplified expression for the total time of the trip is d) 160x + 800 divided by 2x + 10.
To find the total time of the trip, we need to calculate the time it takes for the first half of the distance and the time it takes for the second half of the distance, and then add them together.
Let's start with the first half of the distance. The time it takes to travel the first half of the distance is given by the formula:
Time = Distance / Speed
So for the first half of the distance, the time is:
Time = (160/2) / x = 80 / x
Now let's move on to the second half of the distance. The speed for the second half of the distance is x+10 km/h. So the time it takes to travel the second half of the distance is:
Time = Distance / Speed
Time = (160/2) / (x+10) = 80 / (x+10)
Now we add the times for the first and second halves of the distance together to get the total time of the trip:
Total Time = 80 / x + 80 / (x+10)
To simplify this expression, we find a common denominator and combine the fractions:
Total Time = (80(x+10) + 80x) / (x(x+10))
Total Time = (80x + 800 + 80x) / (x(x+10))
Total Time = (160x + 800) / (x(x+10))
Therefore, the correct simplified expression for the total time of the trip is option d) 160x+800 divided by 2x+10.